Exponential solution of the f(R) gravity with Maxwell term and g -essence

Abstract

In this paper, we consider the f(R) model of gravity with a Maxwell term FµνF µν and g -essence in four dimensions together with a homogeneous, isotropic and flat FriedmanRobertson-Walker universe. As a particular case, g -essence includes two important models such as k -essence and f -essence. For this model, a system of equations of motion is found, an exponential solution is constructed, scalar and fermion potentials are reconstructed, and energy conditions are obtained and investigated. These conditions impose very simple and independent of the model boundary on the behavior of the energy density and pressure, since they do not require a definite equation of state of matter. For the model under consideration, the energy conditions NEC, WEC, DEC are realized, and the SEC condition is violated. We found the parameter of the equation of state ω = −1 and the deceleration parameter q = −1 , which value corresponds to the accelerated expansion of the universe.